The rules for what goes here are the rules of the room. It has to work on one phone passed round a table. It has to be understood without being explained, by somebody who has had two pints and is not concentrating. And it has to be over before the next round arrives, because a game that outlasts a round is a game nobody finishes.
That rules out almost everything and leaves the classics, which is the point. These games are old because they work.
Hi-Lo
The card game every pub in the country has played for a drink. A card is face up. Higher or lower. Get it wrong and you are done, and a tie counts as wrong, because that is how it is played when there is a round on it.
Shuffling.
Playing it in a room rather than on your own? Open the big-screen version. Same game, sized for a television, and it runs off the arrow keys so nobody has to walk over to the screen.
It survives because the maths is doing something your gut disagrees with, all evening, and your gut never learns. This one deals from a real deck without putting the cards back, so when you go out it can tell you exactly how many of the cards left were on your side. Not a fresh-deck estimate. The count in front of you at the time.
The odds are not shown while the card is live, on purpose. Printed above the buttons they would turn it into a calculator, and nobody has ever argued about a calculator.
After that
Short, classic, and playable one-handed. Nothing that needs an account, an app, or a tutorial. If a game needs a tutorial it has already lost the table.
Meanwhile the pub quizzes are the other half of the same evening, and every milestone birthday book has a table-games section in the back of it already.